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An equivalent representation of the Brown-Resnick process

Author

Listed:
  • Engelke, S.
  • Kabluchko, Z.
  • Schlather, M.

Abstract

Brown and Resnick (1977) introduce a max-stable process that is obtained as a limit of maxima of independent Ornstein-Uhlenbeck processes. As shown in Kabluchko et al. (2009) this process is dissipative and it therefore admits a mixed moving maxima representation. We show that the distribution of the spectral functions in this representation equals a well-known diffusion, namely a standard Brownian motion with drift conditional on taking negative values only. This can be used for fast simulation methods.

Suggested Citation

  • Engelke, S. & Kabluchko, Z. & Schlather, M., 2011. "An equivalent representation of the Brown-Resnick process," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1150-1154, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1150-1154
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    Citations

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    Cited by:

    1. Wang, Yizao, 2018. "Extremes of q-Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2979-3005.
    2. Enkelejd Hashorva & Zuoxiang Peng & Zhichao Weng, 2016. "Higher-order expansions of distributions of maxima in a Hüsler-Reiss model," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 181-196, March.
    3. Das, Bikramjit & Engelke, Sebastian & Hashorva, Enkelejd, 2015. "Extremal behavior of squared Bessel processes attracted by the Brown–Resnick process," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 780-796.

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